Theorem 3eltr3i

Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017)

	Ref	Expression
Hypotheses	3eltr3i.1	⊢ 𝐴 ∈ 𝐵
	3eltr3i.2	⊢ 𝐴 = 𝐶
	3eltr3i.3	⊢ 𝐵 = 𝐷
Assertion	3eltr3i	⊢ 𝐶 ∈ 𝐷

Proof

Step	Hyp	Ref	Expression
1		3eltr3i.1	⊢ 𝐴 ∈ 𝐵
2		3eltr3i.2	⊢ 𝐴 = 𝐶
3		3eltr3i.3	⊢ 𝐵 = 𝐷
4	1 3	eleqtri	⊢ 𝐴 ∈ 𝐷
5	2 4	eqeltrri	⊢ 𝐶 ∈ 𝐷